The Serbian spent the majority of last season sidelined with a troubling hamstring injury, but returned to Klopp’s first-team squad for the closing stages.
Grujic was criticised for a strong tackle that left Crystal Palace centre-back James Tomkins injured in May, and then picked up a suspension for two yellow cards at the summer’s European U21 Championship.
Lining up for the Reds this pre-season, the 21-year-old provoked ire from Palace manager Frank de Boer for a lunge at Wilfried Zaha, with the Dutchman saying it was “not appropriate.”
Addressing that challenge and Grujic’s questionable approach off the ball, Klopp agreed that this was a flaw in his game.
“I didn’t see it properly at the time but I heard it could have been a red card,” he told the Liverpool Echo.
“That’s not good. For Marko, it’s something that he has to change.
“He’s a fantastic player, a really skilled boy. Tall, quick, talented footballing wise, all good.
“But in these defensive situations, you always need to be early enough there so you are close enough to make a challenge and not a foul.”
This is something Klopp is not only looking for Grujic to improve, using 18-year-old right-back Trent Alexander-Arnold as another example from training.
“I said it to the players after a session when we had a little situation with Divock [Origi] and Trent,” he added.
“It’s about coming too late, switching off the machine, trying to sort a situation in which you were late in mind. I hate that.
“When that happens you need to run, not foul. Make more steps, go, go, go. For me it’s always a bit lazy.”
Grujic has found himself in the margins since making the £5.1 million move from Red Star Belgrade in 2016, but can hope for a strong campaign in 2017/18.
The midfielder has clearly settled in well with the group, and particularly fellow Balkan duo Dejan Lovren and Lazar Markovic, after a year spent adjusting on Merseyside.
But while he has proved his potential as a top-class midfielder, Grujic is clearly still a work in progress.